Is the median of set S even?

1. Set S is composed of consecutive odd integers

2. The mean of set S is even

Oa is

I think there is some problem with OA here.

Using only statement II we can solve this Q as follows:

Assuming

I. the set as {2,4,6} -------statement II required

Mean = 4 , even

Median = 4 even

II. Set as {2,4,6,8}

Mean = 5

Median = 5

III. Set {1,3,5,7} -------statement II required

Mean = 4

Median = 4

Hence we do not require the info provided in statement I and we can solve with statemetn II only. Can anybody comment on this ?